The first property is not only related to privacy/storage issues, but also speed, as any re-training on the source data would make the approach much slower.
The motivation behind the third property is latency and privacy. For large batch sizes, one has to wait for a certain number of samples, leading to delays, or club samples from multiple users, which may have privacy concerns.
The last property is motivated by the fact that different test instances/batches may come from very different distributions, which will adversely affect the performance of the model. Figure REF  compares the SITA setting with other TTA settings in literature.
Online methods which use large batch sizes, like TENT [1]}, improve performance by evaluating one corruption type at a time (single distribution), and resetting the model for the next corruption type. When evaluated by shuffling all 15 corruption types in the CIFAR-10-C [2]} dataset (mixed distribution), their performance drops considerably, as shown in Figure REF .
